TY - JOUR

T1 - Non-perturbative solution of matrix models modified by trace-squared terms

AU - Klebanov, Igor R.

AU - Hashimoto, Akikazu

N1 - Funding Information: DemeterfiD, . Gross and A. Polyakov for useful discussionsT. his work was supported in part by DOE grant DE-FG02-91ER40671t,h e NSF PresidentiaYl oung Investigator Award PHY-9157482, James S. McDonnell Foundationg rantNo. 91-48, and an A.P. Sloan FoundationR esearchF ellowship.

PY - 1995/1/23

Y1 - 1995/1/23

N2 - We present a non-perturbative solution of large N matrix models modified by terms of the form g(Trø4)2, which add microscopic wormholes to the random surface geometry. For g < gt the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ eα+ø. For g = gt we find a different universality class, and the string susceptibility exponent agrees for any genus with Liouville theory where the interaction term is dressed by the other branch, eα-ø. This allows us to define a double-scaling limit of the g = gt theory. We also consider matrix models modified by terms of the form gO2, where O is a scaling operator. A fine-tuning of g produces a change in this operator's gravitational dimension which is, again, in accord with the change in the branch of the Liouville dressing.

AB - We present a non-perturbative solution of large N matrix models modified by terms of the form g(Trø4)2, which add microscopic wormholes to the random surface geometry. For g < gt the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ eα+ø. For g = gt we find a different universality class, and the string susceptibility exponent agrees for any genus with Liouville theory where the interaction term is dressed by the other branch, eα-ø. This allows us to define a double-scaling limit of the g = gt theory. We also consider matrix models modified by terms of the form gO2, where O is a scaling operator. A fine-tuning of g produces a change in this operator's gravitational dimension which is, again, in accord with the change in the branch of the Liouville dressing.

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U2 - https://doi.org/10.1016/0550-3213(94)00518-J

DO - https://doi.org/10.1016/0550-3213(94)00518-J

M3 - Article

VL - 434

SP - 264

EP - 282

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

SN - 0550-3213

IS - 1-2

ER -